CFD MODELLING AND EXPERIMENTS ON AERATOR FLOW IN...

CFD MODELLING AND EXPERIMENTS

ON AERATOR FLOW IN CHUTE

SPILLWAYS

Penghua Teng

October 2019

TRITA-ABE-DLT-1937

ISBN 978-91-7873-313-2

© Penghua Teng 2019

PhD thesis

Hydraulic and Hydrologic Engineering

Department of Sustainable Development, Environmental Science and Engineering

(SEED)

Royal Institution of Technology (KTH)

SE-100 44 STOCKHOLM, Sweden

Reference to this thesis should be written as: Teng, PH (2019) “CFD Modelling and

Experiments on Aerator Flow in Chute Spillways” TRITA-ABE-DLT-1937.

CFD modelling and experiments on aerator flow in chute spillways

i

SAMMANFATTNING

Ett flodutskov är en typisk komponent hos vattenkraftdammar och som syftar till att släppa ut dimensionerande vattenföring. På grund av den stora fallhöjden hos många höga dammar är flödeshastigheten i utskovskanalen ofta högre än 20 m/s. Följaktligen är utskovsstrukturen oftast sårbar för kavitationsskador. Att lufta vattenströmmen är ett effektivt sätt att eliminera eller mildra skadorna. En luftningsramp är en anordning som blandar in luft i vattenflödet och är en ingenjörsmässig åtgärd för att motverka kavitationsskadorna.

Luftinblandning avser intensivt luft-vattenutbyte och involverar en process med luftinträngning, transport och infångning av luft i immobila fickor i strömningsvägen. På grund av det komplexa fenomenet är det fortfarande en utmaning att undersöka det växelvisa mekaniska beteendet mellan luft och vatten. Det är grundläggande att förstå flödesbeteenden nedströms av luftningsrampen eftersom luften blandas i vattnet och kan sedan avges till atmosfären. Denna avhandling undersöker egenskaperna hos luftningsflödet med både beräkningsmetoder (Computational Fluid Dynamics – CFD) och avancerade labbförsök.

CFD-metoden presenterade tre stycken tvåfasmodeller för att beskriva luftningsflödena, nämligen s.k. Volume of fluid (VOF), Mixture Model och Two-Fluid Model (TFM). De tillämpas och utvärderas med data från prototyputskov och även genom jämförelser med experimentella data. VOF modellen leder till rimliga resultat avseende både vattenflöde och luftmängd. För att förutsäga luftkoncentrationsfördelning och luftbubblors transportprocesser är TFM överlägsen andra metoder (modeller) eftersom den inkluderar krafter som verkar på luftbubblorna. Modellen överskattar dock fortfarande luftinnehållet nära utskovsbotten. Baserat på uppgifter av ett prototyputskov i Sverige tillämpas och jämförs de tre modellerna.

Penghua Teng TRITA-ABE-DLT-1937

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Fysiska modellförsök genomförs vanligtvis för att undersöka egenskaper hos luftningsrampen. På grund av skaleffekter kan resultaten leda till avvikelser i flödesbeteenden jämfört med prototypen. Således blir CFD-modellering ett alternativt verktyg när orsaken till skillnaden söks. Baserat på fältförsök i ett flodutskov appliceras CFD för att reproducera flödesbeteenden; avvikelser mellan modellförsöken och prototypobservationer visas. CFD, som utförs i prototypmått, visar liknande flödesegenskaper som i prototypen men skiljer sig från dem i modellen. En förklaring till avvikelserna diskuteras i termer av flödesegenskaper, ytspänningens effekt i modellförsöken och förutsättningen för luftinträngning genom den fria vattenytan.

Experiment utförs i labbmiljö för att studera luftningsflödet i en ränna. Fyra bildbaserade mättekniker – det vill säga hastighetsmätning med höghastighetspartikelfotografering (High-Speed Particle Image Velocimetry, HSPIV), skuggrafisk bildmetod (Shadowgraphic Image Method, SIM), bubbelspårningsmetod (Bubble Tracking Method, BTM) och bubbelbildshastighetsmetod (Bubble Image Velocimetry ,BIV) – används. Studien fokuserar på frågor som rör karakteristiska lägen för vatten-luftgränssnitt, tolkning av utvärderingsprocessen för luftbubblor som släpper från spetsen av luftkaviteten, identifiering av sannolika medelvärden för karakteristiska lägen av nära den fluktuerande fria vattenytan och att erhålla hastighetsfältet från både vatten- och luftflöde och egenskaper hos luftbubblor i strömmen. Tillämpningen av dessa tekniker leder till en bättre förståelse av tvåfasflödets egenskaper hos luftningsrampen.

Nyckelord: luftningsramp, kavitation, luftinträngning, tvåfasflöde, VOF, Mixture Model, Two-Fluid Model, luftkavitet, kavitetslufttryck, luftkoncentration, skuggrafisk bildmetod , hastighetsmätning med höghastighetspartikelfotografering, bubbelspårningsmetod.


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ABSTRACT

A chute spillway is a typical component of large dams for discharging floods. Because of the high water head, the flow velocity in the chute is often in excess of 20 m/s. Consequently, the structure is usually prone to cavitation damages. Flow aeration is evidenced to efficiently eliminate or to mitigate the damages. An aerator is a device that entrains air into the water flows and is an effective technical measure to counter the cavitation damages.

Aerator flow includes intense air-water exchange and involves a process of air entrainment, transport, and detrainment. Because of the complex phenomena, it is still a challenge to investigate the behaviors of interaction between air and water. It is fundamental to understand the flow behaviors downstream of the aerator. This thesis investigates the aerator flow features using both the Computational Fluid Dynamics (CFD) and advanced measurement techniques.

The CFD method presents three two-phase flow models to describe the aerator flows, namely, the Volume of Fluid Model, the Mixture Model, and the Two-Fluid Model. They are applied and evaluated via practical engineering projects and experimental data. The Volume of Fluid model leads to reasonable results regarding the water flow discharge and flow fields. For predicting the air concentration distribution and air bubble transport processes, the Two-Fluid Model is superior to others because it includes forces acting on the air bubbles. However, the model still overestimates the air content near the chute bottom. Based on the aerator flow from a chute spillway in Sweden, three two-phase flow models are applied and compared.

Physical model tests are commonly conducted to investigate aerator flow features. Because of the scale effects, the results


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may lead to a discrepancy in the flow behaviors compared with the prototype. Thus, CFD modeling becomes an alternative tool when seeking the reason for the difference. Based on the aerator flow in a real spillway, CFD is applied to reproduce the flow; the discrepancy between the model tests and prototype observations is evidenced. The results show similar flow features with the prototype but differ from those of the model tests. An explanation for the discrepancy is discussed in terms of flow features, effect of surface tension in model tests, and the prerequisite for air entrainment of the free-surface flow.

Laboratory experiments are conducted to study the aerator flow

in a chute. Four image-based measurement techniques－ i.e., high-speed particle image velocimetry (HSPIV), shadowgraphic image method (SIM), bubble tracking method (BTM), and

bubble image velocimetry (BIV)－ are employed. The study focuses on issues of exploring characteristic positions of water-air interfaces, interpreting the evaluation process of air bubbles shed from the tip of the air cavity, identifying the probabilistic means for characteristic positions near the fluctuating free surface, and obtaining the flow field both water flow and air bubbles features of the aerator flow. The application of these techniques leads to a better understanding of two-phase flow characteristics of the chute aerator.

Keywords: Spillway Aerator, Cavitation, Air Entrainment, Two-phase Flow, VOF, Mixture Model, Two-Fluid Model, Air Cavity, Cavity Air Pressure, Air Concentration, Shadowgraphic Image Method (SIM), High-speed Particle Image Velocimetry (HSPIV), Bubble Tracking Method (BTM)


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ACKNOWLEDGEMENTS

First of all, I would like to express my deep gratitude to Professor James Yang, my main supervisor, at Royal Institute of Technology (KTH), Stockholm, who has given me invaluable advices, guidance and selfless assistance in my research and helped me establish a network with researchers and consultants in Sweden, Switzerland and China including Taiwan. Thank you for your patient supervision and devoted efforts with the manuscripts.

I am thankful to Professor Anders Wörman, my co-supervisor, for your support and giving me the freedom to carry out the research at KTH.

I am grateful to Professor Cheng Lin and Dr. Ming-Jer Kao at National Chung Hsing University, for your kind arrangements and guidance during my stay in Taiwan. I enjoyed the time with your team in the laboratory.

I would like to thank my colleagues Ida Morén, Shuang Hao, Yuejun Chen, Brian Mojarrad, Joakim Riml, Luigia Brandimarte and Xiao-Liang Ma at KTH and Qiancheng (Kevin) at LTU for the friendly atmosphere and assistance with various matters. Thanks also go to Aira Saarelainen, Merja Carlqvist, Britt Aguggiaro and Anders Ansell for administrative help.

In form of applied research, modeling projects were carried out for Sweco/Uniper, HydroTerra/Fortum and Vattenfall. Supports from Pierre-Louis Ligier, Fredrick Marelius, Finn Midböe and Marcus Bergman are acknowledged. I express also my thanks to Carl-Oscar Nilsson, Uniper, and Jonas Persson, Norconsult, for the unforgettable field visit you arranged and for pleasant trips in China.

For the successful collaborations, I and James are indebted to professors and friends at Haute Ecole d'Ingénierie et d'Architecture de Fribourg (HEIA-FR), Fribourg; Institute of Water Resources & Hydropower Research (IWHR), Beijng; H


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-ohai University, Nanjing; Sichun University, Chengdu, Tsinghua University, Beijing and Électricité de France (EDF), Le Bourget du Lac, and to friends at Vattenfall R&D, Uniper and Luleå University of Technology (LTU).

Finally, I thank my beloved wife, Zhen, for your kind support and understanding and for filling happiness in my life. I want also to express my thanks to my parents for your selfless love, eternal support and everything you have done for me.

The study, as part of a research project entitled “Hydraulic design of chute spillway aerators”, is funded by Swedish Hydropower Centre (SVC). SVC has been established by Swedish Energy Agency, Energiforsk and Svenska Kraftnät, together with Luleå University of Technology (LTU), Royal Institute of Technology (KTH), Chalmers University of Technology (CTH) and Uppsala University (UU). Sara Sandberg, previously at SVC and now at Fortum, is acknowledged for project co-ordinations.


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LIST OF PAPERS

This Ph.D. dissertation, comprising both numerical simulations and laboratory experiments, is based on the following publications. They are denoted as Paper I to VII.

Paper I Teng, P.H. & Yang, J. (2016). CFD modeling of two-phase flow of a spillway chute aerator of large width. Journal of Applied Water Engineering and Research, 4(2),

163‒177.

Paper II Yang, J., Teng, P.H. & Lin, C. (2019). Air-vent layouts and water-air flow behaviors of a wide spillway aerator. Theoretical & Applied Mechanics Letters, 9(2),

130‒143.

Paper III Teng, P.H., Yang, J. & Pfister, M. (2016). Studies of two-phase flow at a chute aerator with experiments and CFD modelling. Modelling and Simulations in Engineering, Volume 2016, Paper ID 4729128.

Paper IV Yang, J., Teng, P.H. & Zhang, H.W. (2019). Experiments and CFD modeling of high-velocity two-phase flows in a large chute aerator facility. Engineering Applications of Computational Fluid Mechanics, 13(1), 48–66.

Paper V Yang, J., Teng, P.H. & Xie, Q.C. (2018). Modelling of air demand of a spillway aerator with two-phase flow models. 2nd Intl. Symp. on Hydraulic Modelling and

Measuring Technology, May 30‒June 1, 2018, Nanjing, China.

Paper VI Teng, P.H. & Yang, J. (2018). Modeling and Prototype Testing of Flows over Flip-Bucket Aerators. Journal of Hydraulic Engineering, 144(12), 04018069.

Paper VII Yang, J., Lin, C., Kao, M.J., Teng, P.H. & Raikar, R.V. (2018). Application of SIM, HSPIV, BTM, and BIV techniques for evaluations of a two-phase air-water chute aerator flow. Water, 10(11), 1590.


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The author’s contribution to each paper is as follows: Paper I. Participation in problem conceptualization and formulation, literature review, numerical setup, numerical simulations, result analyses, participation in manuscript preparation and revision and participation in reply to reviewers

Paper II. Participation in problem conceptualization and formulation, literature review, numerical setup, numerical simulations, result analyses, participation in manuscript preparation and reply to reviewers

Paper III. Problem conceptualization and formulation, literature review, data collection, numerical setup, numerical simulations, result analyses, manuscript preparation, participation in manuscript revision and reply to reviewers

Paper IV. Participation in problem conceptualization and formulation, literature review, participation in data collection, numerical setup, numerical simulations, result analyses, participation in manuscript preparation, revision and reply to reviewers

Paper V. Problem conceptualization and formulation, literature review, data collection, numerical setup, numerical simulations, result analyses, manuscript preparation and conference presentation.

Paper VI. Participation in problem conceptualization and formulation, literature review, numerical setup, numerical simulations, result analyses, participation in manuscript preparation and revision, reply to reviewers

Paper VII. Participation in problem formulation, participation in experiments and follow-up of result analyses.

During the past few years, the author has also participated in other research projects. The related publications are not included in the dissertation but listed here for those who are interested.


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Paper A. Yang, J., Liu, T., Dai, W.H. & Teng, P.H. (2018). Transient water-air flow and air demand following an opening outlet gate. Modelling and Simulations in Engineering, Volume 2018, Paper ID 3194935.

Paper B. Yang, J., Andreasson, P., Hagström, C.-M. & Teng, P.H. (2018). The Tale of an Intake Vortex and Its Mitigation Countermeasure: A Case Study from Akkats Hydropower Station. Water, 10(7), 881.

Paper C. Yang, J., Andreasson, P., Teng, P.H. & Xie, Q.C. (2019) The past and present of discharge capacity modelling for spillways―a Swedish perspective. Fluids, 4, 10.

Paper D. Teng, P.H., Yang, J., Ligier, P.-L., Marelius, F., Pettersson, A., Bard, A. & Kuoljok, U. (2018). Field measurements and CFD modelling of air demand of Moforsen dam spillway. 2nd Intl. Symp. on Hydraulic

Modelling & Measuring Technology, May 30‒June 1, Nanjing, China.

Paper E. Yang, J. & Teng, P.H. (2018). Flow behaviors of Rusfors spillway before and after modifications. 5th

IAHR Europe Congress, 12‒14 June 2018, Trento, Italy.

Paper F. Marelius, F., Yang, J. & Teng, P.H. (2018). Modification of overflow spillway for higher discharge

capacity. HydroVision International, 26‒28 June 2018, Charlotte, USA.

Paper G. Lin, C., Kao, M.J., Yang, J., Teng, P.H. & Raikar, R.V. (2018). Study on probabilistic mean features of lower and upper free-surface profiles and velocity fields of a highly fluctuating free jet over a chute. Journal of Marine Science

and Technology, 26(3), 309‒326.

Paper H. Teng, P.H., Yang, J. & Xie, Q.C. (2019). Improving energy dissipation of a spillway with structural

modifications. IAHR World Congress, 1‒6 September 2019, Panama City, Panama.


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Paper I. Teng, P.H. & Yang, J. (2020). Understanding air-water flows and air venting requirements of a spillway. To be submitted to International Symposium on

Hydraulic Structures, 12‒15 May, Santiago, Chile.

Paper J. Teng, P.H., Yang, J. & Midböe, F. (2020). CFD modeling and prototype observations of geysers from a bottom outlet. To be submitted to ICOLD symposium 2020, New Delhi, India.

Paper K. Yang, J., Andreasson, P., Teng, P.H. & Xie, Q.C. (2019) The past and present of discharge capacity modelling for spillways―a Swedish perspective. Fluids, 4, 10.


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NOTATION

The following symbols are used in the paper:

B = spillway opening width (m)

C = air concentration (−)

Cb = bottom air concentration (−)

CD = drag coefficient (−)

Cwl, Cw2 = non-dimensional coefficients (−)

C0 = discharge coefficient (m0.5/s)

D = bubble diameter (m)

f = (CDRr)/24 (−)

Fa = aerator Froude number (−)

G = interphase force per unit volume of mixture (N/m3)

g = gravitational acceleration (m/s2)

h = approach water depth (m)

H0 = water head (m)

Kaw = interphase exchange coefficient (N·s/m4)

Lj = cavity length (m)

Mwl = wall lubrication force per unit volume of mixture

(N/m3)

�̅�𝑤 = unit normal pointing away from the wall boundary

p = gauge pressure (Pa)

patm = the atmospheric pressure (Pa)

Pv = vapor pressure of water (Pa)

P0 = local pressure including the atmospheric pressure (Pa)

Δp = air pressure drop (Pa)

Qa = air discharge (m3/s)

Qw = water discharge (m3/s)

Re = Reynolds number (−)

Rr = relative Reynolds number (−)


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va = velocity of air phase (m/s)

vw = velocity of water phase (m/s)

V = approach water-flow velocity (m/s)

V0 = average approach water-flow velocity (m/s)

We = Weber number (−)

x = x coordinate (m)

xmwt = mean position of wedged tip of air cavity (−)

xmip = position of mean impingement point (m)

y = y coordinate (m)

Yk%, wai = position for k% intermittent appearance of first

water–air interface

Y(100−k)%, air = (100−k)% fitful appearance of air phase from the

atmosphere in upper gray-level gradient zone

z = z coordinate (m)

ywl = distance to wall boundary (m)

z10, z90 = z coordinate at C = 0.1 and 0.9 (m)

Z = normalized z coordinate (−)

σ = cavitation index (−)

αa = volume fraction of air phase (−)

β = air entrainment coefficient (−)

ρw = water density (kg/m3)

μm = continuum viscosity (Ps·s)

μw = water viscosity (Ps·s)


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CONTENTS

Summary: ............................................................................................... i

Abstract: ............................................................................................... iii

Acknowlegements ............................................................................... v

List of Papers ...................................................................................... vii

Notation............................................................................................... xi

Contents............................................................................................. xiii

Chapter 1 Introduction ......................................................................... 1

1.1 Hydropower Development ...........................................................................1

1.2 Background .......................................................................................................3

1.2.1 Cavitation Damage .....................................................................................3

1.2.2 Chute Aerator .............................................................................................4

1.2.3 Aerator Flow ...............................................................................................7

1.3 Objective ............................................................................................................8

1.4 Thesis Disposition ..........................................................................................9

Chapter 2 Literature Review ................................................................ 11

2.1 Physical Model Tests of Aerator Flows ................................................. 11

2.2 Measurement Techniques for Aerator flows ....................................... 12

2.3 Application of CFD Methods to Aerator Flows .................................. 12

Chapter 3 CFD Modeling of Flows in a Large Width Aerator ............ 15

3.1 Background .................................................................................................... 15

3.2 VOF Model .................................................................................................... 16

3.3 Numerical Results and Aerator Modification ..................................... 17

3.3.1 Spillway Discharge Capacity .................................................................. 17

3.3.2 Air Flow Field .......................................................................................... 17


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3.4 Effect of Aerator Vent Layout .................................................................. 19

3.4.1 Layout Categories .................................................................................... 20

3.4.2 Performance of Aerators ........................................................................ 21

3.4.3 Remarks ..................................................................................................... 23

Chapter 4 Application and Modification of Two-Fluid Model ........... 25

4.1 Two-Fluid Model .......................................................................................... 25

4.2 Modeling of Two-phase Flow at a Chute Aerator .............................. 25

4.2.1 Interphase and Interfacial Forces ......................................................... 26

4.2.2 Results ....................................................................................................... 27

4.3 Improvement of Two-Fluid Model ......................................................... 29

4.3.1 Modified Drag Coefficient ..................................................................... 30

4.3.2 Wall Lubrication Force ........................................................................... 31

4.3.3 Large Chute Aerator Experiment ......................................................... 31

4.3.4 Air Concentration and Downstream Decay ........................................ 32

4.4 Modeling Aerator Flow by Mixture Model ........................................... 34

4.4.1 Mixture Model.......................................................................................... 34

4.4.2 Results and Remarks ............................................................................... 35

Chapter 5 Modeling and Prototype Testing of Flows over Flip-Bucket

Aerators ............................................................................................... 37

5.1 Spillway of Gallejaur Dam ......................................................................... 37

5.2 Physical Model Tests and Prototype Observations ........................... 38

5.2.1 Model Tests .............................................................................................. 38

5.2.2 Prototype Observations .......................................................................... 41

5.3 Numerical Simulations ............................................................................... 43

5.4 Results and Reflections .............................................................................. 44


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5.4.1 Results ....................................................................................................... 44

5.4.2 Some Reflections ..................................................................................... 46

Chapter 6 Case Studies ....................................................................... 49

6.1 Torpshammar Dam ..................................................................................... 49

6.2 Moforsen Dam .............................................................................................. 51

6.3 Results ............................................................................................................. 53

6.3.1 Air flow conditions in Torpshammar Dam ........................................ 53

6.3.2 Air flow conditions in Moforsen Dam ................................................ 55

6.4 Conclusions ................................................................................................... 57

Chapter 7 Measurement Techniques for Evaluations of a Chute

Aerator Flow ....................................................................................... 59

7.1 Introduction ................................................................................................... 59

7.2 Measurement Techniques ......................................................................... 60

7.2.1 High-Speed Particle Image Velocimetry (HSPIV) ............................. 60

7.2.2 Shadowgraphic Image Method (SIM) and Bubble Tracking

Method (BTM) ....................................................................................................... 61

7.2.3 Bubble Image Velocimetry (BIV) ......................................................... 62

7.3 Experiment Setup and Conditions ......................................................... 62

7.3.1 Experiment Setup .................................................................................... 62

7.3.2 Experiment Conditions .......................................................................... 63

7.4 Results ............................................................................................................. 63

7.4.1 Approach Flow as well as Free and Sliding Jet................................... 63

7.4.2 Shedding Process of Air-Bubbles from Tip of Air Cavity ............... 64

7.4.3 Characteristics of Free Surface Position .............................................. 66

7.4.4 Instantaneous and Mean Velocity Fields Measured by BIV ............ 67


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7.4.5 Construction of Two-Phase Velocity Field ......................................... 68

8. Conclusions ..................................................................................... 71

References ........................................................................................... 75


1

1 INTRODUCTION 1.1 Hydropower Development

Hydropower is power generated from moving water and is widespread thanks to its advantages of being clean, sustainable, and reliable. In terms of avoiding the emissions of greenhouse gases, hydropower has one of the lowest lifecycle CO2 emissions among all electricity sources. It is also the world’s largest source of renewable electricity generation.

Hydropower has been used to produce electricity for over 130 years. The first hydropower plant was put in operation in Wisconsin, USA, in 1882. In the first half of the 20th century, USA and Canada were global leaders of hydropower engineering. The Hoover Dam, located on the Colorado River and generating 1,345 megawatts (MW), was the world’s largest hydroelectric plant in 1936. After the 1950s, hydropower was developed mainly in Canada, the USSR, and Latin America. During the last few decades, Brazil and China have taken the lead in hydropower development. The Itaipu Dam, straddling Brazil and Paraguay, began operation in 1984 at 12,600 MW; the Three Gorges Dam in China was commissioned in 2008 at 22,500 MW.

Today, hydropower technology development takes place all over the world. In 2017, clean electricity generated by hydropower reached 4,185 terawatt hours (TWh) and global hydropower installed capacity rose to 1,267 gigawatts (GW).

Sweden is one of the top 20 countries in terms of installed hydropower capacity. An abundance of river streams connecting with more than 100,000 lakes gives the country a vast hydropower potential. The first hydroelectrical power station began its operation in 1882. The pioneering construction of large dam facilities dates


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back to as early as the 1910s, during which Porjus, Trollhättan, and Älvkerleby, the first large dams, were built.

Hydropower developed rapidly after the 2nd World War and reached its peak during the 1950s and 1960s. The economic potential of hydropower in the country amounts to approximately 95 terawatt hours (TWh), up to 75% of potential sources were exploited. The remainder, i.e., Vindelälven, Pite älv, Kalix älv, and Tome-Muonio älv, are protected from development by law due to environmental considerations. The total installed hydropower capacity amounts to 16,200 MW, and the electricity generation varies between 60 and 70 TWh in a normal year, which accounts for 40–50% of the total power production in the country (Paper C).

In the country, approximately 1,000 hydropower dams of varying sizes and ages exist. The large dams are mostly located in northern Sweden. According to the International Commission on Large Dams (ICOLD), a dam height of more than 15 m is defined as a large dam. There are approximately 190 large dams in the country, 80% of which are embankment dams with an impervious core.

The Lule älv is the largest river in Sweden. It has 15 large dams, ten of which are located north of the Arctic Circle. They produce almost 10% of the hydroelectric power in the country. The highest dam, Trägslet, is a 122-m embankment dam on the Dalälvan river. Harsprånget is the largest power plant at 945 MW, which operates under a 107-m water head and a 1,040 m3/s turbine flow rate. The largest hydropower reservoir is Vänern with a 9,400 Mm3 active storage volume.

Even with proven experience in hydropower, there are still significant opportunities for upgrading the capacity of


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the existing dams in the country. Flood-releasing structures are conventionally built according to the dam-safety guidelines that are available at the time of dam construction.

1.2 Background

A chute spillway is a typical flood-release structure in hydropower dams. It releases flows and conveys water over the crest to the riverbed downstream of a dam, particularly during flood seasons. It also prevents damage in the river bed that could otherwise threaten the dam safety. For a large dam, the flow velocity in the chute spillway often exceeds 20 m/s, which may result in cavitation damages in the concrete surface of the spillway surface. As a result, the damages may threaten dam safety.

1.2.1 Cavitation Damage

Cavitation is a phenomenon that occurs in a place where the pressure is sufficiently low. It is a process in which the liquid phase transfers to the formation of small vapor-filled cavities. The cavitation index σ is a crucial parameter when evaluating the occurrence of cavitation. Its expression is written as follows:

𝜎 = 𝑃0−𝑃𝑣

𝜌𝑤𝑉02/2

(1)

where V0 = averaged approach water-flow velocity, ρw = water density, Pv = vapor pressure of water and P0 = local pressure including the atmospheric pressure. If the value of P0 is close to the minimum value of σ, then the pressure at that point will not decrease any further.

Cavitation is an undesirable occurrence because it induces a great deal of noise, damage to components, vibrations, and a loss of efficiency. Cavitation damages often occur in such devices as propellers, pumps, and turbines. The


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damages are observed in hydraulic structures as well. Kramer (2004) summarized the cavitation damages on spillways and bottom outlets from 1935 to 1983. Most of the damages occurred due to small σ values (σ < 0.2). Based on observations in prototype spillways, specifically lager dams, a high-speed flow and low pressures are the main reasons for low σ values.

A more acceptable mechanism of cavitation damage is that microjets are created by the collapse of a single bubble in a wall region, which causes microcracks in the wall surface (Falvey, 1990). When cavitation occurs near the concrete surface of a spillway, it induces the formulation of vapor bubbles. The bubbles are then dissolved in the water and carried away by the flow. Consequently, the surrounding pressure of the bubbles increases, which makes the bubbles no longer sustainable and causes them to implode. The implosions occur at a high frequency with an extremely high pressure of up to 1,500 MPa (Lesleighter, 1988) and countlessly impact the concrete surface. This process results in fatigue failure of the concrete materials, which then creates the microcracks in the surface. After some time, these undesired cracks will cause an elongated hole. As time elapses, the hole becomes larger, with the high-speed flow impacting its downstream end.

For preventing cavitation damages, several methods have been investigated, such as avoiding low values of σ, increasing the strength of concrete materials and entraining air into water flows in spillways (Hamilton, 1983; Grein, 1974; Elder, 1986).

1.2.2 Chute Aerator

Bradley (1945) and Warnock (1947) first noted the concept that used entrained air to reduce cavitation damages in spillways. Peterka (1953) and Russell and


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Sheehan (1974) conducted experimental tests on concrete materials and noted that an air content of 1–2% substantially reduced the cavitation damages, and with more than 5–7%, no damages were observed. From prototype observations, Chen et al. (2003) mentioned that the cavitation damages were obviously mitigated when the air concentration in the vicinity of the wall was in the range of 1.5–2.5%. The damages completely disappeared if the concentration reached 7–8%.

An aerator is a cost-effective device that artificially supplies air into the water flow in a spillway. It is placed where the cavitation damage may occur. In 1961, the effectiveness of aeration was observed in the Grand Coulee Outlet Works (Colgate and Elder, 1961). The first installation of an aerator was at the spillway of Yellowtail Dam (Borden et al., 1971). Since then, aerators have become widespread.

An aerator contributes to raising the air concentration of the water flow in a chute spillway. When the water flows through the aerator, a free jet is generated, and turbulent eddies in the lower jet surface effectively entrain air. An air cavity is formed underneath the jet. During the entraining air by the jet, the pressure in the cavity drops below the atmospheric pressure. As a result, a pressure difference exists between the cavity and the atmosphere, which allows the air from the atmosphere to be sucked into the cavity via the aerator system. Figure 1.1 shows the principle of an aerator.

The type of an aerator is typically a groove (air duct), deflector, offset, or a combination of these (Vischer et al., 1982). Figure 1.2 shows its different types. The function of a groove is to distribute air through the entire width of the aerator, a deflector leads water away from the chute bottom, and an offset prolongs the jet trajectory and enlarges the air cavity, which prevents an aerator from su-


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Figure 1.1. Principle of an aerator

Figure 1.2. Types of aerator: basic types and their combinations


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bmerging at low Froude numbers.

1.2.3 Aerator Flow

The two-phase water-air flow is generated downstream of an aerator, which entrains air into the lower edge of the water flow in a chute spillway. The entrained air travels with the water flow in form of air bubbles. The air bubbles are transported downstream of the aerator. Downstream of the impinging location, the air bubbles rise as they move downstream, which is due to both the buoyancy and the pressure gradient. As a result, a portion of the air bubbles detrains in the flow direction, which lowers the air content near the bottom. Further downstream, the air content reaches a state of equilibrium in the far field of the flow. The air content near the bottom helps eliminate cavitation risks. The air entrainment, bubbles transport, and air detrainment are the features of an aerator flow, which is a complex process of interaction between the water and air.

For a better understanding of the aerator flow, researchers classify commonly the flow into three flow zones, as illustrated in Figure 1.1. The approach flow zone is upstream of the aerator; the cavity zone and far-field zone are separated by the reattachment point, which refers to the maximum pressure position on the chute bottom.

Conventionally, physical hydraulic tests are a primary tool for studying the aerator flow. As complement, CFD is an alternative in multiphase flow modeling. Both approaches are undoubtedly complementary to one another. CFD simulations allow obtaining, in detail, air-water flow fields of aerated flows, which facilitates understanding the effects of the governing parameters in a project.


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1.3 Objective

This thesis uses mainly numerical method to gain a better understanding of aerator flows. The studies adopt different multiphase flow models to reproduce the aerator flows. The Volume of Fluid (VOF) model, Mixture model, and Two-Fluid model (TFM) are all used. The aim is to obtain a reliable CFD approaches that represent the features of aerator flows.

For evaluating the performance of an aerator, it is essential to understand the air flow field in the aerator system, especially for unusually large width aerators. Furthermore, the effect of practice aerator configurations on the air flow field is also a practical issue for engineering projects, which needs to be investigated to suggest a desirable design (Paper I and II).

An aerator flow involves intense air-water exchange and air transport processes, which should be considered when formulating CFD models. The forces governing air bubbles’ motion must be modeled. Then, the performance of CFD models is evaluated based on the characteristic parameters, i.e., air entrainment rate, air-concentration distribution, and air-cavity properties. The simulated results are discussed and compared with the experimental data (Paper III, IV, and V).

Physical model tests and prototype observations are conducted to investigate aerator flows. A scale model suffers from the scale effects, which consequently leads to discrepancy in behaviors between the model and the prototype. This issue appears when studying an aerator flow in the Gallejaur spillway, discussed in Paper VI. A numerical model is then employed to help to seek the reason.


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Four measurement techniques, i.e., high-speed particle image velocimetry (HSPIV), shadowgraphic image method (SIM), bubble tracking method (BTM), and bubble image velocimetry (BIV) are applied to visualize the flow field of an aerator flow in a chute, which is discussed in Paper VII.

1.4 Thesis Disposition

The thesis is structured as follows. Chapter 1 is the introduction and background. Chapter 2 gives a brief literature review of aerator flows, which introduces studies based on both the experimental tests and numerical simulations. Chapter 3 employs the VOF model to reproduce the air flow field of the largest single-opening spillway in Sweden. Some results are compared with the experimental data. Based on the numerical results, the effect of aerator configurations is studied. Chapter 4 shows the capacity of the TFM and its development. The numerical results are then compared with the experimental data. In Chapter 5, discrepancy between the experimental tests and the prototype observations is observed. The utilization of the CFD method helps to seek the reason for the discrepancy. Chapter 6 summarizes the case studies that quantify air demand of spillways during releasing floods. Finally, Chapter 7 describes the application of measurement technologies to aerator flows, i.e., SIM, HSPIV, BTM, and BIV.


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2 LITERATURE REVIEW

An aerator flow is a typically two-phase flow with intense air entrainment, air bubbles transport, and air detrainment. Because of the complex phenomenon with high flow velocity, it is still challenging to understand the features of an aerator flow. This chapter reviews briefly the investigations of aerator flows. Physical model tests are still the primary method of exploring flow behaviors, while CFD methods have become another tool during the last two decades.

2.1 Physical Model Tests of Aerator Flows

Extensive experiments were conducted of chute aerators over the last 40 years. Pan et al. (1980) and Pinto et al. (1982) first evaluated the performance of an aerator using air entrainment coefficient β = Qa/Qw, where Qa = air discharge and Qw = water discharge. Further studies were conducted by Rutschmann (1988), Chanson (1989), Rutschmann and Hager (1990), and Kökpinar and Göğüş (2002). They put forward a linear relationship between β and cavity length (Lj). The effects of the aerator geometry parameters on β were conducted by Pinto and Neidert (1983), Rutschmann and Hager (1990), and Pfister and Hager (2010 a, b).

The definition of β does not account for the streamwise air transport which is described by the distribution of air concentration C, and bottom air concentration Cb. Chanson (1989) and Kramer (2004) investigated the streamwise air transport partially along the far-field flow zone downstream of chute aerators. Kramer and Hager (2005) and Pfister and Hager (2010a) focused on the air bubble rise velocity in turbulent flows as a relevant parameter for air detrainment in the mixture-flow region. Willhelms (1997) and Pfister and Hager (2010a, b) studied the characteristics of C and Cb downstream of chute


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aerators. They conducted systematic model tests, including data analysis of the spatial C distribution in both near and far aerator fields. The key parameters that governed the air transport downstream of an aerator included approach flow Froude number, chute slope, and deflector angle.

2.2 Measurement Techniques for Aerator flows

In the past decades, nonintrusive measuring techniques, such as particle image velocimetry (PIV), HSPIV, BIV, SIM, and BTM, have found their use in investigating two-phase flow fields. These techniques avoid influencing the flow conditions, which significantly enhance the measurement precision and experimental quality. Bercovitz et al. (2016) conducted a large-scale PIV to explore the surface velocity field of a plunging water jet from a sharp-crested weir. They aimed to study the nappe trajectory and characteristic length, along which the energy dissipation became prominent. Ryu et al. (2007) developed the BIV method, which measured the velocity in the mixture by incorporating PIV into SIM. Kashima et al. (2007), Mori et al. (2007), and Mori and Kakuno (2008) investigated air bubble sizes and the void fraction ratio of regular breaking waves during an air entrainment process using the tracking technology combined with SIM. These studies gave support to the techniques when investigating aerator flows. Lin et al. (2008) applied the BIV and HSPIV methods to obtain the velocity fields of the aeration region in a flow at a drop structure. In Papers VII, the authors showed the applications of these measurements and techniques to an aerator flow in a flume.

2.3 Application of CFD Methods to Aerator Flows

The fast growth in computational power and commercialization of advanced software suited for


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solving and visualizing complex flows has contributed to the successful spread of CFD in civil engineering. Various types of two-phase flows have been frequently encountered in hydraulic flow modeling.

As far as both safety and cost are concerned, the accurate prediction of a two-phase flow, either steady or transient, is of interest and desirable. Over the past few decades, several typical two-phase models have been developed and improved (Hirt and Nichols, 1981; Hibiki and Ishii, 2000; Kolev, 2005; ANSYS, 2015; Özkan et al., 2016). These included the Volume-of-Fluid (VOF) Model, Mixture Model, and Two-Fluid Model (TFM).

Aerator flows are an air-bubble flow, occurring at a high-speed flow velocity. It poses a challenge to numerical predictions, since the flow velocity often exceeds 20 m/s and can reach 45 m/s in large dams. The high velocity enhances the exchange between the air and water, which makes the air transport process intensive. This implies that formulations of the phase interactions become complicated in an aerator flow. The main reason for this is the lack of prototype measurement data for numerical model calibration and verification.

The VOF Model has been used to simulate aerator flows (Kökpınar and Göğüş, 2002; Deng et al., 2005; Liu and Yang, 2014; Jothiprakash et al., 2015; Rahimzadeh et al., 2015). Aydin and Ozturk (2009) and Zhang et al. (2011) employed the Mixture Model to investigate an aerator flow. They found that the model gave the desired ability to simulate aerator flows, especially in high air-concentration regions. These studies concentrated on both experimental and prototype data and showed that the model represented reasonable bottom pressure and air cavity profiles. However, criticism was raised by Chanson and Lubin (2010), who discussed Aydin and Ozturk’s approach of verifying the numerical model.


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They questioned the procedure of model verification and validation using a single parameter, i.e., the air-flow rate. Instead, it should be based upon the detailed air-water flow properties at the spillway aerator and independent datasets.

The Two-Fluid Model is also an alternative model for describing aerator flows. Unlike the VOF model, it models the interactions between air bubbles and water, including the phase drag force, the turbulent dispersion force, etc. In related studies, numerical results are compared with the experimental data (Xu et al., 2001; Zhang, 2008). These studies show the potential of modeling aerator flows and further motivate examinations and evaluations of the Two-Fluid Model.


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3 CFD MODELING OF FLOWS IN A LARGE WIDTH AERATOR

This chapter consists of two parts: Paper I and II. Paper I focuses on reproduction of the aerator flow of a prototype spillway with a large width aerator in Sweden. Numerical modeling is used to describe the features of the two-phase flow at the aerator in terms of β, pressure field, and C. The simulations evaluate the performance of the aerator with a specific layout. Based on the results, the layout of the vents shows a significant effect on the performance of the aerator. Consequently, a modified layout of the vents is then designed, and its performance is compared with the original one.

Paper I demonstrates that the layout of the vents influences the performance of the aerator. In Paper II, a further study investigates the effect of vent layouts, involving two categories of eight different layout configurations. Based on the numerical results, the performances of the aerators are evaluated by parameters such as β, the pressure distribution, Lj, the black water length, and the averaged air concentration distribution.

3.1 Background

In Sweden, the width of most high-head spillways is in the range of 10–15 m. The Bergeforsen dam has the largest single chute spillway opening (Figure 3.1). The chute spillway has a width of 25 m. An aerator with 13 air vents is designed in the chute to avoid the risk of cavitation. Its width is 35 m.

Because of the unusual width of the aerator, the air flow field in the duct can exhibit a non-negligible difference across the chute. As a result, the values of β, Lj, and the pressure in the duct may be over or underestimated using commonly used formulas. Furthermore, this would lead t-


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(a) Spillway aerator (b) Aerator shaft

Figure 3.1. Spillway of Bergeforsen Dam (photo: James Yang)

o a deteriorated performance of the aerator. The degree of deterioration could be significant, which jeopardizes the aerator’s operation.

A 1:50 scale physical model is built to investigate the water discharge of the spillway and its flow features. However, due to the scale effects, the characteristics of the aerator flow is not reproduced correctly in the model. To complement the physical model tests, 3D CFD numerical modeling is employed to describe the aerated flow in the chute spillway.

3.2 VOF Model

For modeling the aerator flow, a two-phase model is required. The VOF model is then used in this study. This model is probably the most common method for modeling two immiscible fluids. Each phase in the model is represented by its fraction volume in a computational cell of the domain. Water is usually treated as the primary phase and air as the secondary phase. A set of momentum equations are shared by the two fluids of water and air. In a cell, the water and air have the same velocity, pressure, and other turbulence properties. More details of the VOF model are given in Paper I.


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3.3 Numerical Results and Aerator Modification

3.3.1 Spillway Discharge Capacity

Both the physical and numerical models evaluate the spillway discharge capacity. The spillway discharge is expressed as follows:

𝑄𝑤 = 𝐶0𝐵𝐻01.5 (2)

where C0 = discharge coefficient, B = spillway opening width, and H0 = water head. The results show the relationship between Qw and C0, where C0 increases with Qw. The relative errors between the physical and numerical results are below 5%. It implies that the numerical model can reproduce reasonably the spillway flow upstream of the aerator.

3.3.2 Air Flow Field

The physical model tests focused mainly on evaluating Qw. No tests are made concerning the characteristics of the aerator flow. The numerical simulations are responsible for representing the flow features in terms of the governing the parameters, including β, the pressure distribution in the duct, and the C distributions, listed in Paper I.

Figure 3.2 shows the instantaneous air flow field in the duct and air cavity. The results indicate that the air flow field is not uniform in the duct. In the cavity, the airflow field is characterized by three large circulation zones that occupy almost the entire width of the chute. Due to the large aerator width, the air flow behavior is not as optimal as the designer wished; the air vent configuration is mainly accountable for this result.

The numerical results indicate the undesired air flow field in the duct and cavity, which is caused by the layout of t-


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Figure 3.2. Instantaneous air flow field in the duct and cavity (Qw = 1500 m3/s)

-he vent. As a result, it limits the air supply capacity of the aerator.

The numerical results indicate the undesired air flow field in the duct and cavity, which is caused by the layout of the vent. As a result, it limits the air supply capacity of the aerator. To improve the situation, a modification is made by re-arranging the air vents while the other parts of the aerator remain unchanged. The total air vent area (13 m2) and each vent width (1.0 m) remain the same (Figure 3.3).

Figure 3.3. Modified air vent layout


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The numerical results of the modified layout show that the uniformity of the flow field is improved (Figure 3.4) in both the duct and the cavity. While the air still flows into the duct from the cavity, its influence on the duct flow eases due to the reduction in the vent area close to the wall. Some air circulations still exist in the cavity, but a more uniform air flow field is observed throughout the majority of the cavity. Furthermore, the calculations show that the total air supply capacity of the modified aerator is increased by approximately 33%, which is favorable for the operation.

Figure 3.4. Instantaneous air flow field in the duct and cavity

3.4 Effect of Aerator Vent Layout

For a large width aerator, the previous results indicate that the aerator’s vents layout has a significant effect on the air flow field in both the duct and cavity. Once the vent layout is modified, reciprocal adjustments exist between the jet behavior and air-pressure field in the cavity, thus leading to considerable differences in the flow features. Therefore, based on the geometry of the chute spillway in Bergeforsen dam, a further study (Paper II) is motivated to evaluate the effects of different vent configurations on the aerator’s performance. For each


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configuration, only the layout of the vents is changed, while the air shaft and the total area of the vents remain the same.

To model the aerator flows in this study, the TFM is employed. The model allows the exchange behaviors to be formulated between the air and water phases. The details of the model are stated in the next chapter. The upstream velocity inlet of the computational domain corresponds to Qw = 711 m

3/s at a 3-m partial gate opening. At the aerator offset, the resulting approach flow velocity is V = 16.63 m/s, the approach water depth is h = 1.3 m and the aerator

Froude number Fa = V/(gh)0.5 = 4.38, where g = gravitational acceleration.

3.4.1 Layout Categories

There are two typical categories illustrated in Figure 3.5. Category I includes four single openings. Type A is a rectangle opening with a constant height. The openings of the other three types increase in area from the sidewall to the center plane. Category II is a series of segmented vents with the same heights. For Type E, each vent has the same width. In Types E, F, and G, there are 17 vents with the same number as the prototype aerator. More details of the geometry parameters are listed in Paper II.

Figure 3.5. Types of air vent layout


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Types A and E act as a reference in each category. For the remaining types, the area close to the sidewall is smaller than that of the reference type. The reason for reducing the area is on the basis of the previous result in Paper I, which indicates that a reduction of the area close to the sidewall improves the airflow condition in the duct.

3.4.2 Performance of Aerators

Air-flow rate

Table 3.1 lists the values of β and Qa. The entire air supplied system consists of the air shaft and the air duct. For a given shaft, β represents the effect of the vent layout. In Category I, Types A and B lead to almost the same results. There is an apparent decline in β for Type D due to the narrow vent close to the wall. In Category II, Types E, F, and G give rise to comparable results, in which Type H shows an obvious augmentation because of the rearrangement of the vents with a large rectangular vent in the middle.

Table 3.1. Summary of Qa and β results for the air-vent layouts

Type A B C D

Category I Qa (m3/s) 235.4 236.8 214.4 203.4 β (%) 33.1 33.3 30.1 28.6

Type E F G H

Category II Qa (m3/s) 219.6 220.3 214.7 239.0 β (%) 30.8 30.9 30.2 33.6

Air-pressure distributions

The time-averaged value of pressure drop (Δp) along the duct’s centroid is shown in Figure 3.6. Δp is defined as the difference between the atmospheric pressure (patm) and the gauge pressure (p). The two categories demonstrate a similar Δp tendency. Δp is high close to the sidewall and is low in the central part.


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The prototype measurements of the aerator flow in the spillway of Foz do Areia Dam are cited as comparison (Pinto et al., 1982; Pinto and Neidert, 1982; Pinto, 2018). The width of the spillway chute is 70.6 m, and the aerator is simply an offset with a deflector, without any vents as in Bergeforsen. During the measurements, the air shafts are all open to the atmosphere and the cavity air pressure along the offset is measured. Figure 3.7 plots Δp along the chute at Qw = 1470 m

3/s. It is obvious that Δp exhibits a monotonous decrease from the sidewall to the chute center.

(a) Category I

(b) Category II

Figure 3.6. Changes of Δp (time-averaged value) along aerator duct


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Figure 3.7. Field measured Δp variation across Foz do Areia aerator

Although the pressure in this prototype measurement is not intended for a direct comparison, with the exception of the near-wall pressure rise, the simulated results also display a declining trend towards the center and are consistent with the measurements.

3.4.3 Remarks

In addition, more parameters, i.e., the vent air-flow distribution, Lj, black water length, and C distributions are investigated to reflect the effects of vent layouts in Paper II. Due to the large width aerator, the air-pressure distribution is unfavorable and limit the air flow capacity of the aerator. To counteract the undesirable situation, the vent area should be gradually augmented towards the middle so that more air penetrates towards the chute center.

The study helps to understand the effects of the layout of air vents on the performance of the aerator in a large width chute spillway. It is also advisable to make sure that the aerator not only operates satisfactorily at one flow discharge but within the selected range of discharges.


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4 APPLICATION AND MODIFICATION OF TWO-FLUID MODEL

In the previous chapter, the VOF model is employed to represent the features of the aerator flow in Bergeforsen dam. This chapter, in combination with the different experimental tests, focuses on evaluating the capability of the TFM to represent aerator flows. The simulations are based on laboratory experiments; the numerical results are then compared with the experimental data.

4.1 Two-Fluid Model

An aerator flow is a typical bubble flow with an intense exchange between the air and water. Unlike the VOF model, the TFM is a Euler-Euler approach, which is based on ensemble-averaged mass and momentum equations for each phase. The model allows for formulating the interphase forces and interfacial forces, which mathematically represents the exchange behaviors between the air and water and the forces acted on the bubbles. The details of the equations are given in Paper III.

In the TFM, the air bubbles are assumed to be spherical. The air bubble diameter is a crucial parameter for the TFM, which is included in the formulations of the forces in the form of a given value. The experimental tests in this chapter do not provide any systematical measurements of air bubble sizes. Based on the previous studies of aerator flows, bubble diameters D = 0.5, 1.0, 2.0, 3.0, and 4.0 mm are used in following numerical simulations.

4.2 Modeling of Two-phase Flow at a Chute Aerator

Hydraulic model tests of an aerator were conducted in a flame 0.3 m wide and 6.0 m long at VAW, ETH, and


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Zurich (Pfister and Hager, 2010 a, b). The configuration of the aerator includes a deflector and a groove. The geometric parameters are described in Paper III.

4.2.1 Interphase and Interfacial Forces

In an aerator flow, air is transported in form of air bubbles. The momentum exchange behaviors between the air bubbles and water play a vital role in air bubble movements. In the TFM, the interphase and interfacial forces are formulated to describe the exchange behaviors between the air and water phases.

Interphase force G consists of water-air friction, pressure, cohesion, and other effects. It is written as follows:

𝐺𝑎𝑤 = −𝐺𝑤𝑎 = 𝐾𝑎𝑤(�̅�𝑎 − �̅�𝑤) (3)

where va = velocity of air phase, vw = velocity of water phase, and Kaw = interphase exchange coefficient between water and air phases, which is proportional to the drag function f.

Drag function f governs the motion of air bubbles in a dispersed flow. It acts on the bubbles as a resisting force as a result of the non-uniform pressure distribution of the surrounding water:

𝑓 = 𝐶𝐷𝑅𝑟

24 (4)

where CD = drag coefficient and Rr = relative Reynolds number. The CD model formulated by Schiller and Naumann is used in the numerical simulations.

Interfacial force M refers to the interfacial momentum exchange, which is composed of three terms, namely, the lift force, the turbulence dispersion force, and the virtual mass force. Details of these forces are presented in Paper III.


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4.2.2 Results

In an aerator flow, a large proportion of the air is entrained in the cavity zone. The entrained air is then transported to the far-field zone. During the air bubble transport, most air is detrained in the far-field zone, and the limited air in the immediate vicinity of the chute bottom helps to eliminate cavitation damages.

The performance of an aerator is evaluated by such parameters as β, C distributions, and Cb.

Air Demand

Parameter β reflects the air-entrainment capacity of an aerator. As the black-water core stretches to the end of the cavity, the air supply to the aerator becomes equal to the air entrained in the flow from the lower nappe surface. Table 4.1 shows the β results corresponding to the different D values. With an increase in D, β decreases. D = 1 mm gives the largest difference, while D = 4 mm is close to the experimental result, with a relative error of 9%. All the simulations overestimate the air demand. Therefore, D is a parameter that does affect the air entrainment.

Table 4.1. Values of β in experiments and simulations

Experiments

Simulations

D = 1 mm D = 2 mm D = 3 mm D = 4 mm

Qa 0.0393 0.0629 0.0550 0.0460 0.0430 β 0.228 0.365 0.319 0.267 0.249

Air Concentration

Because of the existence of a black water core, the air supply to the aerator is entrained from the lower nappe surface in the cavity zone. Figure 4.1 illustrates the C distributions at the nappe surface from C = 0.1 to 0.9. z90


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and z10 refer to the z values at C = 0.1 and 0.9. The vertical axis is Z = (z10-z)/(z10-z90). Each diagram compares the C distributions between the experiments and the simulations. The D values vary from 1 to 4 mm.

(a) at x/Lj = 0.33

(b) at x/Lj = 0.66

Figure 4.1. Air concentration distribution at the nappe surface

It is evident that the numerical and experimental results agree well with one another at x/Lj = 0.33, where the x-


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coordinate is placed on the chute bottom (Paper III). The difference is seen for D = 4 mm at x/Lj = 0.66.

Figure 4.2 illustrates the C distributions from the chute bottom to C = 0.9 at x/Lj = 1.3 in the far-field zone. The numerical simulations overestimate the values of C in the vicinity of the chute bottom.

Figure 4.2. C distributions at x/Lj = 1.3

In the TFM, D is a given constant throughout the entire computational domain, which affects the exchange behaviors between the air and water. However, in real aerator flows, the air bubbles’ diameters vary in different flow regions. In the far-field zone, Kramer and Hager (2005) noted that the air detrained after the flow reattachment and the interfacial force between the bubbles and water dominated the process of detrainment in the zone. This implies that the effects of interfacial forces included in the TFM may be underestimated.

4.3 Improvement of Two-Fluid Model

In the above simulations, the drag force model is derived from the motion of a single air bubble. Besides, in the


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impact zone, the jet flow is deflected by the chute base, which affects air bubbles’ movement. The effect of the near-wall interaction on the air bubbles is not considered in the previous model.

For an aerator flow, air bubbles are commonly transported in the form of a cluster. Thus, the movement of a cluster of air bubbles should be considered in the drag coefficient. Meanwhile, the wall lubrication force model should also be included, which describes the effect of the near-wall interaction on the air bubble movements through the jet impact area.

In Paper IV, the TFM is modified based on the above aspects and applied in the following simulations. For evaluating the capability of the model, the numerical results are compared with the experimental data obtained from a large chute aerator facility at the Institute of Water Resources and Hydropower Research (IWHR) in Beijing (Shi, 2007; Zhang et al., 2008).

4.3.1 Modified Drag Coefficient

The Schiller and Naumann (S & N) drag model (1935) is based upon only single bubbles. Due to the associated effects, the CD value for a cluster of bubbles is greater than that for a single bubble (Kolev, 2005). Hence, to calculate CD for a collection of air bubbles, an effective continuum viscosity, μm = μw/(1−αa), where μw = water phase viscosity and αa = volume fraction of air phase, is adopted. The relative Reynolds number for a collection of bubbles is also reformulated as Rr =Dρw|va−vw|/μm, which is a governing parameter in the determination of CD (Ishii and Zuber, 1979; Schiller and Naumann, 1935). Based on the reformulations, the effect of the air-water momentum exchange term is more realistically represented in the Two-Fluid Model. The flow regimes in the dispersed flow are classified in light of Rr (Paper IV).


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4.3.2 Wall Lubrication Force

For a chute aerator flow, a flow jet is generated downstream, which impacts the chute base and the direction of the flow is changed. The change in the flow affects the movement of the air bubbles. The air bubbles are in turn directed and transported along the chute base. In the immediate vicinity of the chute base, the normal balance of drainage around the bubble is interrupted. The drainage rate between the bubbles and base decreases as a result of the no-slip condition. This unbalanced drainage rate generates a hydrodynamic force acting on the bubbles to drive it away from the base. This force is defined as the wall lubrication force. Antal et al. (1991) studied the wall lubrication force and proposed the following expression:

𝑀𝑤𝑙 = 𝐶𝑤𝑙𝜌𝑤𝛼𝑎|(�̅�𝑤 − �̅�𝑎)∥|2

�̅�𝑤 (5)

where |(�̅�𝑤 − �̅�𝑎)∥| = phase relative velocity component

tangential to the wall surface, �̅�𝑤 = the unit normal pointing away from the wall boundary, Cwl = −0.01 and Cw2 = 0.05 are nondimensional coefficients and ywl = the distance to the wall boundary.

4.3.3 Large Chute Aerator Experiment

For achieving close-to-reality conditions, a high water velocity in aerator-flow experiments is needed, which certainly allows for more meaningful comparisons. The aerator experiment tests were performed in a large test rig in Institute of Water Resources and Hydropower Research (IWHR), in Beijing (Shi, 2007; Zhang et al., 2008). The upper chute end is approximately 13 m above the floor, thus producing a flow velocity amounting to 15.4 m/s at the aerator. The experimental data are employed in the following numerical simulations. The


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geometric parameters and measurement methods are presented in Paper IV.

4.3.4 Air Concentration and Downstream Decay

Figure 4.3 shows the C profiles at the cross-sections located in the cavity and far-field zones. For the lower edge of the jet in the cavity zone, the modified model produces a much better match with the experiments; the results of D = 0.5 and 1.0 mm exhibit a better agreement

(a) in the air cavity (b) in the far-field zone

Figure 4.3. C distributions (IWHR experiments)


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than those of D = 2.0 and 4.0 mm. Compared to the cavity zone, the numerical results of the far-field zone are generally more similar to the experimental profiles. The modified model makes stronger predictions than the S & N model and is especially close to the chute base. D = 0.5 and 1.0 mm generates almost the same results, which is in relatively good agreement with the test values.

As previously mentioned, Cb plays a key role in eliminating cavitation damages. It is therefore of practical significance to examine Cb and its streamwise development. Figure 4.4 shows the measured results together with the simulated results. The S & N model clearly overestimates the Cb profile. For the modified model, D = 0.5 and 1.0 mm produce almost identical profiles and generate better results than D = 2.0 and 4.0 mm. Nevertheless, the Cb values from D = 0.5 and 1.0 mm are higher than those of the test results. Due to air detrainment, the air concentrations near the base should approach zero further downstream, as shown by the experiments. However, the numerical modeling generates an almost constant Cb value.

Figure 4.4. Comparisons of Cb between tests and CFD


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The TFM is modified by including the modified drag model and the wall lubrication force. The numerical results are closer to the experimental data, especially in terms of Cb. However, the model still overestimates C in the far-field zone. The constant air bubble diameter in the model accounts for this discrepancy. The model ignores the interaction of the air bubbles, even though the defragmentation and coalescence of bubbles occur in reality as a result of turbulent mixing.

4.4 Modeling Aerator Flow by Mixture Model

In the previous sections, both the VOF and TFM are employed to simulate aerator flows. In addition to these two-phase flow models, the Mixture Model is also a choice for reproducing air-water flow phenomena. In this section, based on the spillway of Bergeforsen dam mentioned in Chapter 3, the aerator flow is modeled by the three models, the results are compared in terms of the air pressure distribution, β, C, and Lj.

4.4.1 Mixture Model

The Mixture Model is a simplified multiphase model. It simulates the different phases (fluid or particulate) by solving the momentum, continuity and energy equations for the mixture, the volume fraction equations for the secondary phases, and the algebraic expressions for the relative velocities. It is used to model multiphase flows where the phases move at different velocities but assume a local equilibrium over short spatial length scales. It also simulates homogeneous multiphase flows with strong coupling and with the phases moving at the same velocity. The Mixture Model differs from the VOF Model in three respects: it allows the phases to interpenetrate, it permits the phases to move at different velocities using the concept of slip velocities, and it considers the interphase


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interaction of mass, momentum and energy transfer. The numerical setup is shown in Paper V.

4.4.2 Results and Remarks

In Table 4.2, comparisons are summarized for Qa and β. For the TFM, the influence of D on Qa and β is limited; the maximum difference is below 5%. Obviously, the VOF Model leads to the lowest Qa value, with the prediction from the Mixture Model falling between them. The difference between the models is considerable; between the VOF and the TFM with D = 1 mm, the maximum discrepancy is 34%.

Table 4.2. Comparison of Qa and β between the three model

VOF Model

Mixture Model

Two-Fluid Model

D = 0.5 mm

D = 1 mm D = 2 mm D = 3 mm

Qa 175.8 204.9 225.4 236.2 228.6 227.8 β 0.24 0.28 0.31 0.33 0.32 0.32

Due to the differences in the formulations of the two-phase flow models, the amount of entrained air differs between the models, which is also evidenced through the cavity air pressure, jet trajectory and spatial distribution of C (in Paper V). The Two-Fluid and Mixture Models give rise to similar results.


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5 MODELING AND PROTOTYPE TESTING OF FLOWS OVER FLIP-BUCKET AERATORS

This chapter aims to understand the two-phase flow features of a unique overflow spillway that incorporates an aerator in each flip bucket in order to aerate the flow and avoid subatmospheric air cavities enclosed by the jets. Physical model tests are conducted but lead to contradicting conclusions compared to prototype observations. As a complement the physical model tests, CFD is employed to seek the reason for the discrepancy. The reason why the physical model tests failed to reproduce the prototype flow behaviors is discussed, and some reflections are made as well.

5.1 Spillway of Gallejaur Dam

Gallejaur dam is located in northern Sweden. Its spillway has two openings with upward-going radial gates, and an artificial discharge canal exists downstream. The spillway layout is shown in Figure 5.1. Each spillway has three flip buckets at two differentiated levels, covering 50% of the opening width (Figure 5.1b). An aeration channel exists in each flip bucket, which supplies air from the space below the chute to the nappe. The flip buckets allow the jets to develop freely, achieving an effective energy dissipation. The geometric parameters are summarized in Paper VI.

(a) spillway layout


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(b) flip buckets with aerators

Figure 5.1. Spillway with flip buckets and aerators at Gallejaur (photo: James Yang)

5.2 Physical Model Tests and Prototype Observations

5.2.1 Model Tests

A 1:40 physical model is built to study the flow features in the spillway (Figure 5.2). It is based on the Froude law

Figure 5.2. Gallejaur, 1:40 physical model of the spillway with flip buckets and aerators (photo:

James Yang)


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of similarity. It includes a 200-m river reach upstream, the spillway structure and a 350-m discharge canal downstream. The flip buckets with aerators in each spillway opening are constructed in light of the prototype configuration. The key issues of concern include the spillway discharge capacity, aerator function, jet behavior, energy dissipation, and stability of the canal rip-rap protection.

For observing the need for aeration, all the three aerators in the left spillway opening were sealed, while those in the right one were left open so that air could come in from b-

(a) Qw = 100 m3/s

(b) Qw = 200 m3/s


40

(c) Qw = 500 m3/s

(d) Qw = 720 m3/s

Figure 5.3. Gallejaur model, flow patterns with and without aeration at FRWL (photo: James

Yang)

elow the chute as in the prototype. The examined reservoir water stage was kept at the full reservoir water level (FRWL). The total flow rate varied in a number of steps, corresponding to a prototype spillway discharge from 100 to 720 m3/s (Figure 5.3).

At lower flow discharges, no difference was observed between the two openings. With an increasing discharge, the middle aerator increasingly spread the water across


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the opening, forming an enclosed water cavity surrounded by a thin water film above. Meanwhile, differences in the jet shapes were obviously evidenced between the two openings at high flow discharges. In the left opening, due to the blocked air passage, the extension of the water jets is limited without any aeration, in both the width and flow directions. A similar situation was also the most obvious for the middle flip bucket.

For the left opening, Figure 5.4 illustrates the air pressure in the cavities below the jets. With an increase in the flow discharge, Δp in the side cavities was larger than in the middle cavity. Until the single-opening flow discharge increased to 360 m3/s, the water jets still had smooth surfaces, and jet oscillation was observed in the flow direction with a low frequency.

Figure 5.4. Gallejaur model, air pressure drop in the cavities

5.2.2 Prototype Observations

Based on the model tests, the spillway structure is refurbished with several upgrade measures, so that


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releasing of the design flood does not threaten the structural safety of the dam. Tests of the prototype flood discharge are performed to check the flow jet behaviors and aerator function (Bond 2006).

The reservoir water-level elevation is 0.37 m below the FRWL. The downstream water stage in the channel is dependent on the discharge. Both spillway openings are tested, but with only one opening at a time. The duration of the free discharge at the full gate opening is approximately 35 min, and the corresponding flow rate is Qw = 320 m

3/s (Figure 5.5).

During the flood tests, all the vents are sealed, and no air is supplied to the flow. When the flow discharge reaches a stable state at the full opening gate, the middle jet covers almost the entire opening width. The black water region exists in the jet and vanishes at approximately 3 m above the water surface. The jet shows a similar shape to the physical model tests, however without fluctuations in

Figure 5.5. Gallejaur spillway, water jets at free discharge 320 m3/s (photo: James Yang)


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the flow direction. Meanwhile, intense air entrainment is observed at the laterals and the lower part of the middle jet. This implies that the air may penetrate the jet, even though no jet air concentration measurements are made. The air pressure in the jet cavities is unclear, but each vent is sealed by a plate that is anchored by small screws. By estimation, the plates could withstand an air-pressure drop of 450–550 N/m2 (prototype dimension). After completion of the flood discharge, the plates remain in position, which implies that no significant air pressure drop occurs in the cavities.

5.3 Numerical Simulations

In terms of jet breakup and stability, the physical model tests and prototype observations lead to contradicting conclusions. CFD is therefore recommended to seek the reason for the discrepancy. The purposes of the CFD simulations are twofold: to reproduce the flow behaviors of the prototype spillway and to clarify, in terms of jet trajectory and aeration, the differences between the models and the prototype.

Figure 5.6. Computational domain


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3D CFD simulations are performed based on the prototype dimensions, as shown in Figure 5.6. The VOF two-phase model is employed to represent the two-phase flow behaviors in the spillway. The setup details are given in Paper VI.

5.4 Results and Reflections

5.4.1 Results

The discharge capacity of the spillway is obtained and compared with the results from the physical model tests. The maximum difference is below 2.5–3.5%, which shows that the spillway flow upstream of the flip buckets is well reproduced in the CFD model.

Figures 5.7a and b show the flow patterns along the center planes of the middle and side flip buckets. Figures 5.7c and d show the profile of the air cavities at the cross-sections located at Lj/3 and Lj2/3 accounted from the lower edges of the aerators. They are colored according to the VOF of the water and air.

From Figures 5.7a and b, the black water zone exists in both the middle and side jets. It is clear that the middle jet begins to break up close to the tailwater surface, while no obvious jet breakup is observed in the side jets. However, intense air entrainment occurs around the impact zone. At the cross-section located at Lj/3 (Figure 5.7c), the air cavity configurations are evident. With an increasing distance from the flip bucket (Figure 5.7d), the water curtain between the middle and side cavities gradually becomes thinner and then breaks up. Further downstream, the water jets break up, and the air enters the cavities through the jets.

The observations of the middle jet breakup imply that air can freely enter the air cavity. Meanwhile, air entrainment exists in the side jets, which means that a limited air exch-


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(a) along middle flip bucket

(b) along side flip bucket

(c) at cross-section Lj/3


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(d) at cross-section 2Lj/3

Figure 5.7. CFD for Gallejaur spillway, behaviors of flow trajectories and air cavity profiles

ange occurs between the atmosphere and the air cavity. Furthermore, the air pressure in the cavities is illustrated in Paper VI, and the results show that no significant pressure change occurs in the cavities.

The CFD simulations show similar results to the prototype observations, i.e., jet breakup, air entrainment of the jets and stable flow trajectories.

5.4.2 Some Reflections

The CFD simulations help understand the flow features of the spillway at Gallejaur dam. But it is still worthwhile to clarify why the model tests failed to reproduce the prototype flow behaviors. The reasons can be explained in terms of flow pattern, scale effects, and prerequisites for air entrainment.

The flow patterns in the spillway are similar to the flow over a Piano Key Weirs (PKW). Many PKW studies are


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conducted in small-scale models and fail to represent the water-air patterns of the cavity and air entrainment phenomenon. Since the physical models of PKWs usually have dimensions smaller than that of an ordinary spillway, it is not clear to what extent the effects of the surface tension and air entrainment affect the physical modeling results.

The physical model of Gallejaur spillway is built based on the Froude law of similarity. The viscous and surface tension forces should be negligible in order to obtain reasonable results. In the physi

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